Revealing thermally driven distortion of magnon dispersion by spin Seebeck effect in ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$

We report a systematic study of the temperature and field dependences of the spin Seebeck effect (SSE) in a bilayer of $\mathrm{Pt}/{\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. An anomalous structure is observed in the magnetic field dependent measurements at temperatures between ∼60 and ∼210 K. Unlike the ordinary SSE signal originating from the bare magnons, which changes sign at ∼95 and ∼266 K, the sign of the anomalies remains unchanged with increasing temperature. Moreover, the anomalies are found to show a temperature-sensitive double-peak structure between ∼116 and ∼143 K. We attribute these anomalies to the contribution from the quasiparticles hybridized between the Gd moment dominated spin wave (α mode) and the transversal acoustic phonon, known as the magnon polarons. Given that the magnon polaron induced anomalies occur at the field where the linear phonon dispersion is tangential to the magnon dispersion curve, we explain these rich phenomena by an increase of the group velocity of the α-mode magnon with increasing temperature and the nonparabolic magnon dispersion of ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. Our results demonstrate that the magnon polaron induced SSE is helpful for the investigation of the magnon dispersion evolution with a simple transport approach.

Figure 1

(a) The XRD $\omega -2\theta$ scan of the GdIG/GGG (111) film. (b) The typical hysteresis loops measured on the GdIG film at three typical temperatures. (c) The magnetization as a function of temperature measured at a magnetic field of 0.05 T. The inset is the blowup around $T_{\mathrm{comp}}$.

Figure 2

(a) Measurement geometry of the SSE in Pt/GdIG/GGG sample. (b) $V$ as a function of $\mathrm{\Delta }T$ for the Pt/GdIG/GGG sample at ${\mu }_{0}H=0.2\mathrm{T}$. (c) $S$ as a function of magnetic field for Pt/GdIG/GGG sample at 75.66, 187.25, and 285.22 K, respectively. (d) Temperature dependence of $S$ for Pt/GdIG/GGG sample.

Figure 3

(a) $S$ of the Pt/GdIG/GGG sample measured at different temperatures. (b) The corresponding blowups of $S$ at different temperatures.

Figure 4

(a) The positions of the anomalous peaks as a function of temperature for Pt/GdIG/GGG sample. For $T\le \sim 108\mathrm{K}$, only one peak appears. For $\sim 108\mathrm{K}<T<\sim 129\mathrm{K}$, the anomalies display a double-peak shape. However, only one peak position can be determined. For $\sim 129\mathrm{K}\le T\le \sim 143\mathrm{K}$, the positions of both peaks can be resolved. For $T>\sim 143\mathrm{K}$, only one peak is observed and the other peak is not observable due to the rapid change of the background signal around the coercivity field. (b) The schematic diagram of the group velocities of the α-mode magnon and TA phonon as a function of wave vector at different temperatures of GdIG film. (c) The schematic diagram of dispersion relations of the α-mode magnon and TA phonon for $T>\sim 108\mathrm{K}$. The black, blue, and red solid curves represent the dispersion curves of the α-mode magnon when the applied field is 0, $H_A$, and $H_B$, respectively. (d) Temperature dependence of the intensity of the anomalous structures.